From David Entwistle@21:1/5 to All on Thu Jul 31 14:02:06 2025
From Amusements in Mathematics by Henry Ernest Dudeney. The book provides
the following information and asks the following question:
This is a new (in 1917) and interesting companion puzzle to the "Fifteen Schoolgirls" and even in the simplest possible for in which I present it
there are unquestionable difficulties. Nine schoolboys walk out in
triplets on the six week days so that no boy ever walks *side-by-side*
with any other boy more than once.
If we represent them by the first nine letters of the alphabet, they may
be grouped on the first day as follows:-
A B C
D E H
G H I
Then A can never walk again side by side with B, nor B with C, nor D with
E, and so on. But A can, of course, walk side by side with C. It is here
not a question of being together in the same triplet, but of walking side
by side in a triplet. Under these conditions they can walk out on six
days; under the "Schoolgirls" condition they can only walk on four days.
It isn't explicit, but I'm sure we are being asked for the six
arrangements of schoolboys.